{
  "id": "1403.5786",
  "version": "v2",
  "published": "2014-03-23T18:35:54.000Z",
  "updated": "2014-11-01T13:41:38.000Z",
  "title": "On a choice of the mollified function in the Levinson-Conrey method",
  "authors": [
    "Sergei Preobrazhenskii",
    "Tatyana Preobrazhenskaya"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT",
    "math.CV"
  ],
  "abstract": "Motivated by a functional property of the Riemann zeta function, we consider a new form of the mollified function in the Levinson-Conrey method. As an application, we give the following very slight improvement of Conrey's result: at least $40{.}883$% of the zeros of the Riemann zeta function are on the critical line. Our choice of the mollified function can be used to improve the recent results of Bui, Conrey and Young, and of Feng slightly, but the computations there are more complicated. Although the improvements are very modest, our construction might be useful in understanding good choices of the mollified function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-23T18:35:54.000Z",
      "title": "Large proportion of the zeros of the Riemann zeta function on the critical line",
      "abstract": "Following the method of Levinson and Conrey and applying an analytic identity we prove that large proportion (at least $47%$) of the zeros of the Riemann zeta function is on the critical line. We briefly discuss a generalization of the argument that leads to the statement that almost all of the zeta zeros are critical.",
      "comment": "10 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-01T13:41:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "large proportion",
      "critical line",
      "zeta zeros",
      "analytic identity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5786P"
    }
  }
}